Kazuhiro KONNO

Email konno(
Complex algebraic geometry
Keywords Algebraic surface, pencil of algebraic curves, singularity
Office Science Building B-448 (Toyonaka Campus)

Algebraic Geometry is a branch of Mathematics studying, by means of algebraic methods, the geometry of figures defined by simultaneous algebraic equations in several variables. You may say that you are not familiar with Algebraic Geometry. But you already know many beautiful plane curves such as an ellipse, a parabola and a hyperbola; they are in fact our jewels --- algebraic varieties. As you learned in high school, various problems on the geometry of plane curves, e.g., how two curves intersect or contact, can be solved by considering simultaneous equations. Studying figures in such a way is nothing but the algebraic geometry. Algebraic equations, however, are not so simple; it is not known so far even how to solve simultaneous quadratic equations, whilst the method for linear equations are well established as you learned in the course of Linear Algebra, and many beautiful algebraic varieties are usually given by quadratic equations. Because in general we cannot draw figures of varieties on the black board, unlike ellipses or parabolas, it requires such and such training in order to be able to touch and feel them. For example, my favorite algebraic surfaces are 4 dimensional objects and, therefore, cannot be realized in our 3 dimensional space. If you are interested in meeting them in reality, the best way is to start and enjoy learning Algebraic Geometry.